The present invention relates to communications signal modulators for improving signal bandwidth in a medium subject to channel fading. More specifically, but without limitation thereto, the present invention relates to a modulator/demodulator for mitigating the effects of channel fading on the amplitude and phase of MQAM communications symbols.
Multiplicative Rayleigh channel fading is a frequent problem in wireless communications. A standard technique for combating such channel instabilities is differential coding. In addition to possessing a reduced sensitivity to channel effects, differentially encoded signals do not require synchronization for suppressed carriers. Thus, they avoid additional noise from devices such as phase-locked loops. Differential encoding is particularly effective when the basic modulation is M-ary phase shift keying (MPSK) in which case it is labeled DPSK (differential MPSK). On the other hand, if the channel is relatively benign and fading is not an issue, one may obtain higher bit rates (as well as an improved SNR performance over MPSK) for an equivalent bandwidth by using M-ary quadrature amplitude modulation (MQAM). A variation, particulary used to combat multiplicative Rayleigh fading while still retaining MQAM, is differential MQAM (i.e., DQAM). In the case of DQAM, the differential encoding removes, or at least mitigates, the effects of channel fading upon the phase component of the MQAM signal. However, the amplitude is still vulnerable to the channel, and one must resort to approximate techniques such as automatic gain control to estimate the magnitude of fading and to extract symbol amplitude. Such methods fail if the fade rate becomes too large. That is, they suffer from a trade-off between the quality of the channel estimation and the speed at which it is tracked. The following examples further clarify the problem of channel fading.
M-ary phase shift keying (MPSK) symbols may be expressed by the formula EQU s=Ae.sup.2.pi.j(m-1)/M =Ae.sup.j.phi..sbsp.m ( 1a)
where
A is real, EQU .phi..sub.m is 2.pi.j(m-1)/M; m=1, . . . , M; (1b) PA1 M is the total number of symbols to be encoded. PA1 .alpha.(t) is a complex function of time t corresponding to channel amplitude and phase distortion caused by channel fading, PA1 s(t) is a symbol received at time t, and PA1 n(t) is channel noise at time t. PA1 A.sub.d (t) is the amplitude at time t, and PA1 .theta.(t) is the phase at time t. PA1 n=1, . . . ,N, and p=1, . . . ,P.
and
A received symbol subjected to multiplicative channel fading may be modeled as .alpha.(t)s(t)+n(t), where
An estimate of the phase of .alpha. may be used to demodulate the MPSK signal, but a rapidly fading channel makes such estimates difficult. Alternatively, the modulation technique may be modified to use a differential MPSK (DPSK) signal EQU d(t)=A.sub.d (t)e.sup.j.phi.(t), (2)
where
Also, d(0) may be assumed known, e.g. d(0)=1, and the current value of d(t) may be defined as a function of its previous value d(t-1) and the current symbol s(t) from equation (1a) by EQU d(t)=A.sub.d (t-1)e.sup.j(.phi.(t)+.theta.(t-1))= s(t)d(t-1)/A(3)
Note that in this case, .vertline.d(t).vertline.=.vertline.s(t)/A.vertline. .vertline.d(t-1).vertline.=.vertline.d(t-1).vertline., i.e., .vertline.d(t).vertline. is constant. The phase of symbol s(t) may be recovered from the phase of received signal d.sub.r (t) times the complex conjugate of d.sub.r (t-1): EQU phase(s(t))=phase(d.sub.r (t)d.sub.r (t-1)) (4)
The phase shift of symbol s(t) is independent of the fading channel to the extent that the phase shift due to the channel given by phase(.alpha.(t).alpha.(t-1) is approximately zero as follows.
Since .alpha.(t) is approximately .alpha.(t-1), EQU .alpha.(t).alpha.(t-1).alpha.(t).alpha.(t).apprxeq..vertline..alpha.(t).ver tline..sup.2
which has zero phase.
MQAM symbols are a combination of amplitude and phase modulation, i.e., EQU s=A.sub.n e.sup.2.pi.j(p-1)/P =A.sub.n e.sup.j.theta..sbsp.p( 5)
where
DQAM is typically implemented by differentially encoding the
phase: EQU d(t)=s(t)d(t-1)/.vertline..vertline.d(t-1).vertline..vertline.,(6a)
and recovering the symbol by ##EQU3## The phase of s.sub.r (t) is virtually independent of channel fading as described above, but the received amplitude .vertline.s.sub.r (t).vertline.=.vertline..alpha.(t)s(t).vertline. requires channel estimation to extract the amplitude of transmitted symbol s(t). This may be done by averaging techniques such as automatic gain control (AGC), but there is a performance tradeoff between averaging over enough symbols to smooth out the dependence on A.sub.n and a short enough time period to track the fading channel.
A continuing need therefore exists for an effective method to mitigate the effects of channel fading on both symbol amplitude and phase.